C1 - Signals

Sound


Frequency (fundamental)	Pitch
Amplitude	Loudness (logarithmic)
Harmonics (details of repetitive pattern)	Timbre (quality)

Speed of sound will affect the frequency, thus affecting pitch.

h h \frac{θ}{2 π} = \frac{t}{T} = A sin (\frac{2 π}{T}) = A sin (2 π f t)

Periodic signals with difference repetitive patterns have different amount/amplitudes of harmonics

A tone with only the first harmonics is a pure tone
A tone with many harmonics is a rich tone

The amplitude-frequency graph
At a given time (cross-section of a spectrogram / function of time) OR average over a long period (generic spectrum)
Each frequency representing a sine wave

Human speech has negligible energy at $f > 4000 Hz$

c = f λ


Radio	1 km $\to$ 1 cm
Visible	400 nm $\to$ 700 nm

Audible spectrum: 20 Hz to 20000 Hz
Best: 1 kHz to 5 kHz
Worst: < 60 Hz OR > 10 kHz
Visible spectrum: 400 to 800 THz

X \cdot H = Y

Speech spectrum: 300 to 3400 Hz
So lowpass filter with $f_{c} \sim 3 kHz$ is used for telephone

Carrier frequencies < 1 GHz
Analog systems
Frequency Division Multiple Access (FDMA)
- Using different frequencies for Frequency Mixing
Suffers from eavesdropping

Phased out in Hong Kong by 1998

s_{A M} (t) = x (t) sin (2 π f_{c} t)

sin (2 π f_{c} t) sin (2 π f_{b} t) = \frac{1}{2} (cos (2 π (f_{c} - f_{b}) t) - cos (2 π (f_{c} + f_{b}) t))


$f_{c}$	Carrier frequency
$f_{b}$	Baseband frequency

Usually $f_{c} > f_{b}$

Multiply baseband with carrier $\to (f_{c} - f_{b}) and (f_{c} + f_{b})$
Multiply modulated signal with carrier again $\to f_{b} and (2 f_{c} - f_{b}) and (2 f_{c} + f_{b})$
Lowpass filtering with cutoff frequency $= f_{b} \to f_{b}$

Size of antenna $\propto λ \propto \frac{1}{f}$